Peel white asparagus with a vegetable peeler from top to bottom, starting below the tips. Cut off any woody ends with a knife.
Place asparagus spears in a large, wide saucepan and pour in enough lightly salted water to just cover. Bring water to a boil; add sugar and salt. Reduce heat; simmer until spears are tender and easily pierced with a knife, 15 to 25 minutes. Drain.
Whisk eggs and flour together in a large bowl. Add milk and 1 pinch salt; whisk into a smooth batter with no lumps.
Melt 1 tablespoon butter in a large nonstick skillet over medium-low heat. Ladle 1/4 of the batter into the skillet. Cook until bubbles form and the edges are dry, 3 to 4 minutes. Flip and cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter, using 1 tablespoon butter to cook each pancake.
Divide asparagus evenly among the pancakes. Wrap pancakes around the asparagus and place on serving plates.
Melt remaining 3 tablespoons butter in the skillet. Add hard-boiled eggs; cook and stir until heated through, 2 to 3 minutes. Stir in parsley. Divide egg mixture evenly over pancakes.